I have a Singer 251-2 machine that I would like to install a Servo Motor on. Will this also require the speed reducer as well?

You do need the speed reducer with the servo motor and everything that you need comes with them. The only thing that a servo motor does is slow down the speed… it has no strength, or torque, at low speeds. The speed reducer (more accurately called a torque creator) does that for you. Those old clutch motors like you have are a killer!!!